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Principal Functions

  • Book
  • © 1968

Overview

Authors:
  1. Burton Rodin

    1. University of California, San Diego, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Leo Sario

    1. University of California, Los Angeles, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: The university series in higher mathematics (USHM)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction: What are Principal Functions?

    • Burton Rodin, Leo Sario
    Pages 1-13

  3. Prerequisite Riemann Surface Theory

    • Burton Rodin, Leo Sario
    Pages 14-37

  4. The Normal Operator Method

    • Burton Rodin, Leo Sario
    Pages 38-80

  5. Principal Functions

    • Burton Rodin, Leo Sario
    Pages 81-137

  6. Capacity, Stability, and Extremal Length

    • Burton Rodin, Leo Sario
    Pages 138-192

  7. Classification Theory

    • Burton Rodin, Leo Sario
    Pages 193-210

  8. Analytic Mappings

    • Burton Rodin, Leo Sario
    Pages 211-231

  9. Principal Forms and Fields on Riemannian Spaces

    • Burton Rodin, Leo Sario
    Pages 232-286

  10. Principal Functions on Harmonic Spaces

    • Burton Rodin, Leo Sario
    Pages 287-304

  11. Back Matter

    Pages 305-347
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Keywords

About this book

During the decade and a half that has elapsed since the intro­ duction of principal functions (Sario [8 J), they have become impor­ tant tools in an increasing number of branches of modern mathe­ matics. The purpose of the present research monograph is to systematically develop the theory of these functions and their ap­ plications on Riemann surfaces and Riemannian spaces. Apart from brief background information (see below), nothing contained in this monograph has previously appeared in any other book. The basic idea of principal functions is simple: Given a Riemann surface or a Riemannian space R, a neighborhood A of its ideal boundary, and a harmonic function s on A, the principal function problem consists in constructing a harmonic function p on all of R which imitates the behavior of s in A. Here A need not be connected, but may include neighborhoods of isolated points deleted from R. Thus we are dealing with the general problem of constructing harmonic functions with given singularities and a prescribed behavior near the ideal boundary. The function p is called the principal function corresponding to the given A, s, and the mode of imitation of s by p. The significance of principal functions is in their versatility.

Authors and Affiliations

  • University of California, San Diego, USA

    Burton Rodin

  • University of California, Los Angeles, USA

    Leo Sario

Bibliographic Information

  • Book Title: Principal Functions

  • Authors: Burton Rodin, Leo Sario

  • Series Title: The university series in higher mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-8038-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1968

  • Softcover ISBN: 978-1-4684-8040-5Published: 27 July 2012

  • eBook ISBN: 978-1-4684-8038-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVIII, 348

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: Originally published by Van Nostrand

  • Topics: Analysis

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